Well I can offer a brief two-pronged answer, though perhaps someone else with more knowledge could go into more detail or have a different answer (since this is largely speculation as the writers intent can't necessarily be known).
Firstly: it most likely is just a random, absurd joke. As its structure and implementation is in-keeping with the traditional Abe Simpsons joke-style harkening back to a bygone past that probably never existed (IE: Germans stole the word "twenty", Onion on my belt which was the style at the time). But that's not a terribly interesting or history based answer so now let us move on to the second part of the question.
Is there any genuine historical reason Abe Simpson has for refusing to recognize Missouri as a state? While it would be absurd to be refusing to recognize it in the 1990's there would in-fact be a long bygone reason for refusing to recognize it and that namely would be the Missouri compromise.
To quickly overview a fairly common piece of US history: the Missouri compromise was a compromise devised around the admittance of Missouri as a new state into the union in 1820. Missouri was to be admitted as a slaveholding state which was upsetting to abolitionists and northern states as it would set a precedence for the expansion of slavery and that it could lead to a dominance of slaveholding states in the senate. Simultaneously Maine (then a part of Massachusetts) was also applying for statehood. The compromise would see Maine's admittance as a free-state as a condition for Missouri's admittance as a slave-state while also cementing a demarcation-line (the Mason-Dixon Line) into popular consciousness. This would ostensibly maintain a balance of federal power between the slave and free-states and hopefully prevent future issues regarding the expansion of slavery (Spoiler alert: it didn't).
So, needless to say: the Missouri compromise was controversial. Many abolitionists in the North were completely opposed to the expansion of slavery in any shape or form, including five representatives from Maine. Who opposed the statehood of Maine on the basis of Maine's statehood being a pretext for the expansion of Southern Slavery. These five representatives (Martin Kinsley, Joshua Cushman, Ezekiel Whitman, Enoch Lincoln, and James Parker) would write to Portland Magazine thusly:
"Restrictions and impediments, in relation to Missouri, were odious, — unconstitutional, — invidious, — and we know not what But, in regard to Maine, she might be loaded down with restrictions, or any and every impediment; and to secure what ? The interests and welfare of Maine? No ; power— a balance of power: and to whom? To the slave-holding States. They say to Maine, ‘You may come into the Union ; we shall be glad to receive you ; you are entitled to admission upon every principle. But, if you do come in, you must bring with you Missouri — slaves and all — not only those which she now has, but all that she may acquire to the end of time."^(1)
So needless to say there were many abolitionists in the North, particularly in Maine who did not want Missouri to be admitted to the Union under such pretenses, even if it meant their own state was not admitted! And from the language of this quote deeming elements of the process unconstitutional (by extension one could safely assume this to mean illegitimate). So it is well-within the realm of historical plausibility for people (particularly abolitionists and Maine abolitionists) to have viewed the admittance of Missouri as unconstitutional and illegitimate both because of the arbitrary restrictions it placed on Maine as well as the extension of an abhorrent system.
But now there is another interesting thread here. In "The Simpsons Movie" released in 2007, Ned Flanders clearly states the four states that border the town of Springfield.
"Ohio, Nevada, Maine, and Kentucky."^(2)
So with this we know that the town of Springfield is established as being within walking distance of Maine. This coupled with Abe Simpsons dubious age and backstory, makes it completely plausible in-universe that Abe was one such Mainer or at least close to such Mainers who were opposed to the admittance of Missouri into the Union. Hence his continued refusal to acknowledge the admittance of a slave-state into the Union.
Sources
^(1.)) https://digitalcommons.library.umaine.edu/cgi/viewcontent.cgi?article=1009&context=mainebicentennial